Galois group of exceptional curves on the generic del Pezzo surface

Xinyu Fang

Galois group of exceptional curves on the generic del Pezzo surface

Algebraic Geometry 2026-04-03 v1 Number Theory

Authors: Xinyu Fang

Abstract

We prove that the Galois action on the exceptional curves on the generic del Pezzo surface of degree $d$ is maximal for all degrees $d$ and over any field $k$ . As a consequence of the case $d=3$ , we deduce that over $\mathbb{F}_q(u)$ , 100% of cubic surfaces have no Brauer-Manin obstruction.

Keywords

del Pezzo surface exceptional curves Galois group Brauer-Manin obstruction cubic surfaces

Cite

@article{arxiv.2604.01497,
  title  = {Galois group of exceptional curves on the generic del Pezzo surface},
  author = {Xinyu Fang},
  journal= {arXiv preprint arXiv:2604.01497},
  year   = {2026}
}

Comments

11 pages

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